A two-inch cube ($2\times2\times2$) of silver weighs 3 pounds and is worth $\$200$. How much is a three-inch cube of silver worth

Answer:

1/15

Step-by-step explanation:

dividend=1/3

divisor=5

since

Dividend ÷ Divisor = Quotient.

1/3 ÷5 = 1/15

Therefore, quotient = 1/15

Answer:

\( \triangle \: A'B'C' \: will \: have : \\ \angle \: A' \: at \: point \: ( - 1 ,\: 1). \\ \angle \: B' \: at \: point \: ( 1,\: 3). \\ \angle \: C' \: at \: point \: ( - 3 ,\: 3).\)

Answer:13.8 is the best answer i could get

Step-by-step explanation:1,077 multiply that × 13.8 =14,862

The scenario described here can be considered an experimental setup.

In this experiment, Kara is manipulating the independent variable, which is the presence or absence of ice cubes surrounding the smaller jars that hold the frogs. By placing ice cubes only in one set of jars and not in the other set, Kara is creating two different conditions: one with a cold environment (ice cubes surrounding the jar) and one without (no ice cubes surrounding the jar).

Kara's objective seems to be to observe the effect of the cold environment on the frogs, as she inserted a thermometer through a hole in the lid of each jar to monitor the temperature.

The setup allows for a comparison between the two groups of frogs: one group was exposed to the cold environment created by the ice cubes and the other group was exposed to a regular room temperature. By comparing the behavior, reactions, or physiological responses of the frogs in the two groups, Kara can draw conclusions about the potential impact of temperature on the frogs' well-being or behavior.

Therefore, this scenario represents an experimental study, as Kara is actively manipulating the independent variable and observing the effects on the dependent variable (the behavior or physiological response of the frogs) to draw conclusions.

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The relative frequency distribution of the three categories includes

We must get percentage of students in Yes (Y), No (N) and No Response (NR) categories to allow us to create the relative frequency distribution for the athletic department.

Data:

The total number of students surveyed is 1000.

The percentage of students who answered Yes will be:

= (Y / Total) * 100

= (733 / 1000) * 100

= 73.3%

The percentage of students who answered No will be:

= (N / Total) * 100

= (162 / 1000) * 100

= 16.2%

The percentage of students who did not respond will be:

= (NR / Total) * 100

= (105 / 1000) * 100

= 10.5%.

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Answer:

x=(-7|0)

y=(0|2)

Step-by-step explanation:

hope it helps ^^

Answer:

1. A=42

L=14

42=W(14)

divide both sides by 14

3=W

2. A=96

L=12

96=W(12)

divide both sides by 12

8=W

3. A=90

L=18

90=W(18)

divide both sides by 18

5=W

4. A=1.50

L=15

1.50=W(15)

divide both sides by 15

0.1=W

Step-by-step explanation:

Answer:

Step-by-step explanation:

The calculated coordinates of point N is  (3, -6)

To find the coordinates of point N, we need to use the fact that LN to NM is 2:1. This means that the distance from L to N is twice the distance from N to M.

Given that

L = (1, -2) and M = (4, -8)

The coordinates is calculated as

N = 1/(m  + n) * (mx2 + nx1, my2 + ny1)

Substitute the known values in the above equation, so, we have the following representation

N = 1/(2  + 1) * (2 * 4 + 1 * 1, 2 * -8 + 1 * -2)

So, we have

N = (3, -6)

Hence, the point is (3, -6)

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Answer:

2 ans ......

Step-by-step explanation:

Solution:

= ³√9-1

= ³√8

= 2 ans....

Answer:

\( \sqrt[3]{9 - 1} = \sqrt[3]{8 } = \sqrt[3]{ {2}^{3} } = + - 2\)

Answer:

60

Step-by-step explanation:

Answer:

Reflection across the x-axis

Step-by-step explanation:

The points are the same, just opposite of one another. The image looks as if it is a reflection. Think of the x-axis like a puddle and the shape looking into it; try to picture the image seeing its reflection to help.

Answer:

Reflection across the x-axis.

Step-by-step explanation:

The triangles mirror each other with the x-axis acting like said mirror.

Step-by-step explanation:

\(y = 2x - 4\)

\(3x + y = 1\)

\(y = 1 - 3x\)

Equating,

\(2x - 4 = 1 - 3x\)

\(2x + 3x = 1 + 4\)

\(5x = 5\)

\(x = 1\)

Placing it,

\(y = 1 - 3( 1)\)

\(y = 1 - 3\)

\(y = - 2\)

Answer:

33

Step-by-step explanation:

Answer:

number n = 8

Step-by-step explanation:

let the number be n then adding it to 10 gives 10 + n

multiplying this by 6 gives 108 , that is

6(10 + n) = 108 ( divide both sides by 6 )

10 + n = 18 ( subtract 10 from both sides )

n = 8

the original number is 8

Answer:

8 1/2

Step-by-step explanation:

She read 8 1/2 pages each day because if you divide 85 by 10 you will get 8 1/2.

Elaine saw statistics showing that union employees make an average of 30 percent more than nonunion workers, so when she was looking for a new job, she looked for one at a company that was unionized. Elaine was motivated by Economic needs.

By economic need Elaine is trying to get a company that would pay her more. Hence the need to go for the Unionized company.

This is given that the Unionized company is said to earn more than the other company. Hence her motivation is due to her economic needs.

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The angle between the laser beam and the building is given as follows:

2.69º.

The three trigonometric ratios are defined as follows:

For this problem, we have that:

Hence the angle is obtained applying the tangent function as follows:

tan(x) = 40/850

x = arctan(40/850)

x = 2.69º.

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a) The probability that the next charge will last less than 2.5 hours is approximately 0.1883.

b) The probability that the next charge will last between 2.8 and 5.2 hours is approximately 0.4859.

c) The probability that the next charge will last more than 2.7 hours is approximately 0.4493.

a) To determine the probability that the next charge will last less than 2.5 hours, we need to calculate the cumulative distribution function (CDF) of the exponential distribution with a mean of 3.9 hours. The CDF of the exponential distribution is given by F(x) = 1 - e^(-λx), where λ is the rate parameter. In this case, λ = 1/3.9 (since the mean is equal to the reciprocal of the rate parameter).

Plugging in x = 2.5 hours into the CDF formula, we get F(2.5) = 1 - e^(-1/3.9 * 2.5) ≈ 0.1883. Therefore, the probability that the next charge will last less than 2.5 hours is approximately 0.1883.

b) To determine the probability that the next charge will last between 2.8 and 5.2 hours, we need to calculate the difference between the CDF values at those two points. Using the CDF formula, we find F(2.8) = 1 - e^(-1/3.9 * 2.8) and F(5.2) = 1 - e^(-1/3.9 * 5.2). The probability between these two points is then given by the difference: F(5.2) - F(2.8) ≈ 0.4859.

Therefore, the probability that the next charge will last between 2.8 and 5.2 hours is approximately 0.4859.

c) To determine the probability that the next charge will last more than 2.7 hours, we subtract the CDF value at 2.7 hours from 1. Using the CDF formula, we find F(2.7) = 1 - e^(-1/3.9 * 2.7). Subtracting this value from 1 gives us approximately 0.4493.

Therefore, the probability that the next charge will last more than 2.7 hours is approximately 0.4493.

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Answer

so if you got 1 candy bar and your friend took 1 candy bar from you how many candy bars do you have left? 0, you have zero

We start by making the substitution $u = y'$. Then, we have $y'' = \frac{du}{dx}$, and we can rewrite the original equation as:

\(��2���2+2�=28�x dx 2 d 2 u​ +2u=28x 2\)

This is a linear homogeneous differential equation with constant coefficients. The characteristic equation is:

\(�2�+2=0r 2 x+2=0\)

which has roots $r = \pm i\sqrt{\frac{2}{x}}$. Therefore, the general solution for $u$ is:

\(�=�12�cos⁡(2�ln⁡(�))+�22�sin⁡(2�ln⁡(�))u=c 1​ x2​\)

​

\(cos( x2​ ​ ln(x))+c 2​ x2​ ​ sin( x2​ ​ ln(x)\))

where $c_1$ and $c_2$ are constants of integration.

To find $y$, we integrate $u$ with respect to $x$. Using integration by parts, we have:

\(�=∫���=∫2�cos⁡(2�ln⁡(�))��′=2\)

\(2�sin⁡(2�ln⁡(�))+�3y=∫udx=∫ x2​ ​ cos( x2​ ​ ln(x))dx ′ =2 2x​ sin( x2​ ​ ln(x))+c 3​\)

where $c_3$ is another constant of integration.

Therefore, the general solution for the original differential equation is:

\(�=22�sin⁡(2�ln⁡(�))+�3+�4�y=2 2x​ sin( x2​ ​ ln(x))+c 3​ +c 4​ x\)

where $c_4$ is a constant determined by the initial conditions of the problem.

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The probability of processing at least 3040 jobs is: P(processing at least 3040 jobs) = 1 - P(processing at most 3039 jobs) = 1 - ∑_(k=0)^3039▒e^(-24x) (24x)^k/k!.By trial and error, we can find that x = 17 servers is the minimum number of servers that meets the requirement.P(processing at least 3040 jobs) = 1 - P(processing at most 3039 jobs) = 1 - ∑_(k=0)^3039▒〖e^(-24*17) (24*17)^k/k!〗≈ 0.950

a. Let x be the number of servers needed to ensure that 95% of jobs are processed in 4 hours.

Since each server takes 20 minutes, then the processing rate is 3 jobs per hour per server. So the processing rate for x servers is 3x jobs per hour.

The total number of jobs arriving in 4 hours is 20*4*λ = 20*4*20 = 1600 (since λ = 20 jobs per hour).So the number of jobs processed by x servers in 4 hours is 3x * 4 = 12x.

So we need to find the smallest integer x such that P(processing at least 95% of the jobs) = P(processing at least 1520 jobs) ≥ 0.95, where 1520 = 0.95*1600.The probability of processing exactly k jobs in 4 hours is a Poisson distribution with parameter λ' = 4*3x = 12x. Therefore, the probability of processing at least 1520 jobs is:

P(processing at least 1520 jobs) = 1 - P(processing at most 1519 jobs) = 1 - ∑_(k=0)^1519▒e^(-λ') (λ')^k/k!.By trial and error, we can find that x = 10 servers is the minimum number of servers that meets the requirement.

P(processing at least 1520 jobs) = 1 - P(processing at most 1519 jobs) = 1 - ∑_(k=0)^1519▒〖e^(-12*10) (12*10)^k/k!〗≈ 0.952.

b. If the time horizon becomes 8 hours, then the total number of jobs arriving in 8 hours is 20*8*λ = 20*8*20 = 3200.So the number of jobs processed by x servers in 8 hours is 3x * 8 = 24x.

So we need to find the smallest integer x such that P(processing at least 95% of the jobs) = P(processing at least 3040 jobs) ≥ 0.95, where 3040 = 0.95*3200.

The probability of processing exactly k jobs in 8 hours is a Poisson distribution with parameter λ' = 8*3x = 24x. Therefore, the probability of processing at least 3040 jobs is:

P(processing at least 3040 jobs) = 1 - P(processing at most 3039 jobs) = 1 - ∑_(k=0)^3039▒e^(-24x) (24x)^k/k!.By trial and error, we can find that x = 17 servers is the minimum number of servers that meets the requirement.P(processing at least 3040 jobs) = 1 - P(processing at most 3039 jobs) = 1 - ∑_(k=0)^3039▒〖e^(-24*17) (24*17)^k/k!〗≈ 0.950.

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a.  At least 124 servers are needed to ensure that 95% of jobs are processed in 4 hours.

b. If the time horizon becomes 8 hours, at least 230 servers are needed to ensure that 95% of jobs are processed.

To find the minimum number of servers over 4 hours needed to ensure that 95% of jobs are processed in that 4 hours

The total number of jobs that arrive in 4 hours, denoted by N, follows a Poisson distribution

μ = λt = 20*4 = 80,

where λ is the arrival rate and

t is the time interval.

The processing time for each job is 20 minutes, so the number of servers needed to process all the jobs within 4 hours is given by

k = ceil(N/(u/3))

where ceil(x) is the smallest integer greater than or equal to x.

To find the value of k that ensures that 95% of jobs are processed in 4 hours, find the smallest integer k

P(N ≤ k; u) = F(k; u) = Σ(i=0 to k) \((e^(-u) * u^i\) / i!) ≥ 0.95

Using a calculator the smallest integer k that satisfies this inequality is k = 124.

Therefore, at least 124 servers are needed to ensure that 95% of jobs are processed in 4 hours.

If the time horizon becomes 8 hours, the total number of jobs that arrive in 8 hours

k' = ceil(N'/(u'/3))

By following the same steps as above, the smallest integer k' that ensures that 95% of jobs are processed in 8 hours is k' = 230.

Therefore, at least 230 servers are needed to ensure that 95% of jobs are processed in 8 hours.

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Answer:

Step-by-step explanation:

The same array can represent both multiplication and division because for multiplication you count all the dots in the array. For division you do the array backward. 81÷9= ?. For this problem you would draw out 9 dots, then adding rows you would count to 81. Once you got to 81, the amount of columns you have is your answer. So for that problem your answer is 9.

Hi there! Use the following identities below to help with your problem.

\( \large \boxed{sin \theta = tan \theta cos \theta} \\ \large \boxed{tan^{2} \theta + 1 = {sec}^{2} \theta}\)

What we know is our tangent value. We are going to use the tan²θ+1 = sec²θ to find the value of cosθ. Substitute tanθ = 4 in the second identity.

\( \large{ {4}^{2} + 1 = {sec}^{2} \theta } \\ \large{16 + 1 = {sec}^{2} \theta } \\ \large{ {sec}^{2} \theta = 17}\)

As we know, sec²θ = 1/cos²θ.

\( \large \boxed{sec \theta = \frac{1}{cos \theta} } \\ \large \boxed{ {sec}^{2} \theta = \frac{1}{ {cos}^{2} \theta} }\)

And thus,

\( \large{ {cos}^{2} \theta = \frac{1}{17}} \\ \large{cos \theta = \frac{ \sqrt{1} }{ \sqrt{17} } } \\ \large{cos \theta = \frac{1}{ \sqrt{17} } \longrightarrow \frac{ \sqrt{17} }{17} }\)

Since the given domain is 180° < θ < 360°. Thus, the cosθ < 0.

\( \large{cos \theta = \cancel\frac{ \sqrt{17} }{17} \longrightarrow cos \theta = - \frac{ \sqrt{17} }{17}}\)

Then use the Identity of sinθ = tanθcosθ to find the sinθ.

\( \large{sin \theta = 4 \times ( - \frac{ \sqrt{17} }{17}) } \\ \large{sin \theta = - \frac{4 \sqrt{17} }{17} }\)

Answer

Answer:

-9x

Step-by-step explanation:

trust me it’s -9x

Answer:

13x - 22

Step-by-step explanation:

combine like terms 8x + 5x= 13x and 15-37= -22, so the simplified expression is 13x-22

To prove that quadrilateral ABCD is a parallelogram, we will use the Single Opposite Side Pair Theorem, which states that if a quadrilateral has one pair of opposite sides that are parallel, then it is a parallelogram.

To prove that ABCD is a parallelogram, we will use the Single Opposite Side Pair Theorem. According to the theorem, if we can show that one pair of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.

Given the information in the problem, we are given that AD and BC are parallel (AD || BC). Now, we need to demonstrate that the other pair of opposite sides, AB and CD, are also parallel.

To prove this, we can use the transitive property of parallel lines. Since AD is parallel to BC and AB is a transversal intersecting these parallel lines, we can conclude that AB is also parallel to BC. Similarly, since AD is parallel to BC and CD is a transversal intersecting these parallel lines, we can conclude that CD is also parallel to BC.

As a result, we have shown that both pairs of opposite sides of quadrilateral ABCD are parallel (AD ||BC and AB||CD). By the Single Opposite Side Pair Theorem, we can conclude that ABCD is a parallelogram.

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Answer:

15.7 cm

Step-by-step explanation:

5 × 3.14

15.7 cm

The probability that a randomly chosen part is defective is 0.16, or 16%.

The probability that a randomly chosen part is defective, we need to use the law of total probability.

Let \($D$\) be the event that a part is defective and let \($M_i$\) be the event that the part came from machine \($i$\), for \($i = A, B, C$\).

Then we have:

\($P(D) = P(D|M_A)P(M_A) + P(D|M_B)P(M_B) + P(D|M_C)P(M_C)$\)

60% of the products come from machine A, 30% from machine B, and 10% from machine C.

Therefore:

\($P(M_A) = 0.6$\)

\($P(M_B) = 0.3$\)

\($P(M_C) = 0.1$\)

The probability of a part being defective is 10% if it comes from machine A, 30% if it comes from machine B, and 40% if it comes from machine C.

Therefore:

\($P(D|M_A) = 0.1$\)

\($P(D|M_B) = 0.3$\)

\($P(D|M_C) = 0.4$\)

Substituting these values into the law of total probability, we get:

\($P(D) = 0.1 \cdot 0.6 + 0.3 \cdot 0.3 + 0.4 \cdot 0.1 = 0.16$\)

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Answer:

y=-5x-3

Step-by-step explanation:

put -1 and 1 in equation and you will get the answer

The equation that best represents a line perpendicular will be y = - 5x - 3. Then the correct option is A.

Let the equation of the line be ax + by + c = 0. Then the equation of the perpendicular line that is perpendicular to the line ax + by + c = 0 is given as bx - ay + d = 0

The equation of the line passing through (-1, 2) and (1, -8). Then the equation of the line will be

y + 8 = [(-8 - 2) / (1 + 1)] (x - 1)

y + 8 = -5x + 5

y = - 5x - 3

The equation that best represents a line perpendicular will be y = - 5x - 3. Then the correct option is A.

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